Method and apparatus to track gain variation in orthogonal frequency division multiplexing (OFDM) systems

ABSTRACT

Gain variations during a packet can lead to significant performance degradation in communications systems that use high order quadrature amplitude modulation (QAM). A method and the associated apparatus track such variations in an OFDM system and completely eliminate any performance degradation. Gain estimation and compensation is employed with the use of pilot subcarriers in the payload of an OFDM data packet. Estimated pilot magnitude ratios are averaged, throughout the processing life of a packet, to yield accurate gain estimations. A gain compensation factor is used to adjust data carriers. An exclusion method is also employed to eliminate pilot carriers which contribute to noise.

RELATED APPLICATIONS

This application is a continuation of U.S. application Ser. No.11/522,793, filed Sep. 18, 2006, which is a continuation-in-part of U.S.application Ser. No. 11/343,736, filed Jan. 30, 2006, which is acontinuation of U.S. application Ser. No. 11/202,930, filed Aug. 12,2005, which claims the benefit of U.S. Provisional Application No.60/601,099, filed on Aug. 12, 2004. The entire teachings of the aboveapplications are incorporated herein by reference.

BACKGROUND OF THE INVENTION

Frequency Division Multiplexing (FDM) is a technology, widely used incommunication systems, which allows for the transmission of multiplesignals simultaneously over a single transmission path. Each signaltravels within its own unique frequency range, or carrier, which ismodulated by the data (i.e., text, voice, video, etc.) to represent theinformation being transmitted.

Orthogonal Frequency Division Multiplexing (OFDM) is a technique whichdistributes data over several carriers that are spaced apart at precisefrequencies. This spacing provides the orthogonality in this techniquewhich prevents the demodulators from seeing frequencies other than theirown.

From a frequency perspective, a typical OFDM packet structure 100 isdivided into subcarriers, as shown in FIG. 1. These subcarriers arefurther classified into pilots (P_(n)) or data (X_(n)). Pilots aresubcarriers whose value is known prior to the transmission of thepacket. Knowing the value of the pilot subcarriers serves as a usefulreference to estimate impairments throughout a packet.

In contrast to the pilot subcarriers, the value of data subcarriers isnot known prior to the transmission of the packet. The data subcarriershold the information which is to be transmitted, and is thereforeunknown prior to transmission. Each data carrier has an associatedpilot, which is typically the pilot that is closest to it in frequency.FIG. 1 shows the four pilots (P₀-P₃) and the associated data subcarriersfor a 802.11 OFDM.

From a time perspective, the OFDM packet 200 is divided into a sequenceof OFDM symbols, as is shown in FIG. 2. At the start of the OFDM packet200 is a training symbol 201, which is followed by a number of payloadsymbols 203(1)-203(n). All subcarriers (pilots and data) in the trainingsymbol 201 are known prior to the transmission of the OFDM packet,wherein, only the pilots are known prior to transmission in the payloadsymbols 203.

In order to distribute and transmit the various OFDM symbols, OFDMsystems may employ a Quadrature Amplitude Modulation (QAM) scheme. A QAMscheme conveys data by changing or modulating the amplitudes of twocarrier waves, in response to a data signal. A typical OFDM transmitterand receiver pair 300 employing a QAM scheme is shown in FIG. 3. A flowof bits to be transmitted from a digital transmitter baseband 304 issplit into two equal parts, therefore generating two independentsignals. The two signals are converted to analog signals via digital toanalog converters (DAC) 306 a and 306 b. The analog signals are thenpassed through low pass filters (LPF) 308 a and 308 b. The two analogsignals are then encoded separately, with one analog signal beingmultiplied 308 a by a cosine wave and the other analog signal beingmultiplied 308 b by a sine wave. The encoded signals are then addedtogether 311, and the combined signal is then passed through a poweramplifier 312 and transmitted with the use of an antenna 313. Thereceiver 302 detects the transmitted signal with the use of an antenna315 and transmits the signal to a radio frequency receiving device 314.The received signal is then separated and decoded with themultiplication of a cosine wave 316 a and a sine wave 316 b. The signalsare then passed through a low pass filter 318 a and 318 b, andthereafter, the signals are digitally transformed with the use of analogto digital converters 320 a and 320 b. Finally, the signals are thensent to the digital receiver baseband 322.

In the radio frequency (RF) portion of the transmitter, electromagneticwaves are generated and transmitted by alternating current fed intoantenna 313. This RF section is also a region that may be susceptible togain variations. Gain variations may be caused by a number of factors,one of which may be thermal changes in the transmitting device. FIG. 4shows a calculated transient electrical response of a self-heatingdevice. The self-heating effect, caused by a temperature rise due to apower dissipation and a temperature dependence of devicecharacteristics, can be regarded as a thermal-electrical feedback insidethe device (f). The y-axis of the plot represents the gain change of thedevice and the x-axis represents normalized time.

As may be seen in FIG. 4, the device is stable, or endures minimal gainvariations with respect to time, when f<1. The device becomes unstable,or endures sustainable variations with respect to time, when f≧1. Thegraphical data illustrates gain changes increasing linearly with timefor f=1, and exponentially with time for f>1.

The effects of gain variations on a signal are also shown in FIGS. 5Aand 5B. In an undistorted QAM constellation, points are usually arrangedin a square grid with equal vertical and horizontal spacing and with thenumber of points on the grid typically being a power of 2, as may beseen in FIG. 5A. FIG. 5B displays a QAM 64 constellation, which may beused to support 48 and 54 Mbps rates in a typical 802.11 transmitter andreceiver pair, with a 0.5 dB gain distortion. As is shown in FIG. 5B,the 0.5 dB gain distortion has caused the constellations of the QAM tobecome blurred and expanded. Distortions may include impairments such asgroup delay, discrete echoes (e.g., reflections, ghosts or multipathdistortion), micro-reflections and amplitude tilt. Distortions such asthe ones previously mentioned are capable of causing serious damage toupstream data. The table below records the signal to noise ratio (SNR)limit that is imposed on a signal due to gain variation or distortion.

Power Amplitude SNR Variation Variation Limit (dB) (dB) (dB) 0.1 0.0538.7 0.2 0.10 32.7 0.3 0.15 29.1 0.4 0.20 26.5 0.5 0.25 24.5 0.6 0.3022.9 0.7 0.35 21.5 0.8 0.40 20.3 0.9 0.45 19.2 1.0 0.50 18.3

As this table shows, a 0.25 dB gain variation in amplitude and a 0.5variation in power will impose a 24.5 dB upper bound on the SNR. A QAM64 or a 54 Mbps system may not function properly with such bounds sincethis system generally needs 27-28 dB in a typical indoor environment.Also, the 802.11 standard transmitter and receiver pair mandates aminimum error vector magnitude (EVM) of 25 dBc. With gain changes of0.25 dB or more, the transmitter will not even meet the EVMspecification (assuming that the transmitter is the source of gainvariation).

Prior art methods of gain compensation have been developed in an attemptto correct the distortion caused by gain variation. Many prior artmethods of gain compensation make use of the training symbols in theOFDM packet to estimate the gain. An estimation may typically be made ata time 0, or once a packet is first received. Thus, many prior artsystems will evaluate the pilots of the training symbol once the packethas first arrived, ‘time zero,’ and estimate a gain variation. The datasubcarriers of the payload symbols are then compensated based on theinitial estimation made at ‘time zero.’ An updated estimation may bemade, again at time zero, once a new packet has been received.

SUMMARY OF THE INVENTION

A method and apparatus for gain compensation of a packet in anorthogonal frequency division multiplexing (OFDM) system is discussed.The system establishing an initial magnitude estimate for a packet,determining a variation in magnitude of the packet over time, andapplying to the packet a gain that varies over time. The gain may bebased on the initial magnitude estimate and the variation in magnitude.The determination of the variation in magnitude may further comprisedetermining a pilot magnitude ratio estimation over time, and computinga pilot magnitude estimation based on the pilot magnitude ratioestimation. The pilot magnitude ratio may be normalized by a lead pilot.Pilot exclusion may also be comprised in the establishment of thevariation in magnitude, wherein a pilot whose magnitude is low inaccordance with an exclusion algorithm. The variation in magnitude maybe updated for every OFDM symbol or alternatively may be updated after apredetermined number of OFDM symbols have been processed. The system maycompute the gain compensation factor by obtaining a ratio of the initialmagnitude estimate and the variation in magnitude. The gain compensationfactor may comprise an operator that returns an index of a pilotassociated with the data subcarrier.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing will be apparent from the following more particulardescription of example embodiments of the invention, as illustrated inthe accompanying drawings in which like reference characters refer tothe same parts throughout the different views. The drawings are notnecessarily to scale, emphasis instead being placed upon illustratingembodiments of the present invention.

FIG. 1 is an illustrative example of an OFDM packet viewed from afrequency perspective;

FIG. 2 is an illustrative example of an OFDM packet viewed from a timeperspective;

FIG. 3 is a schematic of a typical OFDM transmitter and receiver pair300 employing a QAM scheme;

FIG. 4 is a graphical representation of a calculated transientelectrical response of a self-heating device;

FIGS. 5A and 5B are schematics of an undistorted and distorted,respectively, QAM 64 constellation grid;

FIG. 6 is a block diagram of a canonical OFDM receiver;

FIG. 7 is a block diagram of a OFDM receiver according to an embodimentof the present invention;

FIG. 8 is a detailed view of the computational gain estimation andcompensation steps according to an embodiment of the present invention;and

FIG. 9 is a graphical representation of results obtained using methodsand systems according to embodiments of the prior art and the presentinvention.

DETAILED DESCRIPTION OF THE INVENTION

A description of preferred embodiments of the invention follows.

Prior art methods of gain estimation and compensation are generallynoisy. It is possible to degrade the performance of a modem when suchnoisy estimates are used to compensate for gain variations. The noisygain estimates in prior art systems are primarily due to the fact thatall gain estimations are made prior to processing the packet, at ‘timezero.’ Changes in gain may occur over microseconds while packet durationmay occur in milliseconds. Thus, gain variations may radically affect asystem and may also cause mid-packet gain variation, which may bedetrimental to the data packet. Therefore, during the processing life ofthe packet, significant changes in gain may occur. These mid-packetchanges must be accounted for in gain estimation and compensationcalculations.

FIG. 6 displays a canonical OFDM receiver 600. The receiver 600typically first applies a timing and frequency offset correction 601 toa received signal. The timing and frequency offset correction 601 isapplied to the start of an OFDM packet and synchronizes the packet intime and frequency. A Fast Fourier Transform (FFT) is then performed onthe synchronized signal to produce the frequency representation of theOFDM signal comprising pilot and data subcarriers. An equalization 605is then performed to adjust the signal such that all the pilotsubcarriers are of equal value. A phase correction or derotation 607 mayalso be performed to correct rotational distortions. Finally the signalmay be decoded 609 in order to produce bits.

As is shown in FIG. 6, the canonical OFDM receiver 600 does not accountfor mid-packet gain variations. Thus there is no adjustment for gainover the length, or processing life, of an OFDM packet. Furthermore,pilots may be so severely effected by gain variation that their use ingain estimation and compensation calculations may add significant noiseto the estimate. The OFDM receiver 600 does not account for severelydegenerated pilots in gain estimation or compensation calculations.

A system and method of gain estimation and compensation is needed whichmay adjust gain estimations throughout the length or processing life ofan OFDM packet without introducing noise in the system. An embodiment ofthe present invention is to build a gain estimator that eliminates theproblem of gain variation, in the receiver, without causing significantadditional performance loss of its own. The receiver estimates andcompensates for gain variation throughout the length, or processingtime, of the OFDM packet. A method of inclusion/exclusion is alsopresented, where a pilot may be included or excluded based on theseverity of its gain change. Thus, the inclusion/exclusion methodprevents the incorporation of substantially degraded pilots in gaincompensation and estimation calculations.

An important feature of first order OFDM systems is that the frequencyof the OFDM symbols will remain constant over time. Hence, while pilotmagnitudes may change with gain variations, their magnitude ratio willremain constant. Thus, in an embodiment of the present invention, apilot magnitude ratio estimate is obtained for all pilots in eachpayload symbol. The pilot magnitude ratio estimation is obtained througha time average of pilot ratios, rather than the pilots themselves, whichmay be updated for every symbol. Upon obtaining the pilot magnituderatio estimation, the pilot magnitude estimation may be found using anaveraging technique. Finding the pilot magnitude estimation by using thepilot magnitude ratio estimation yields accurate results, as compared toprior art methods, due to the fact that pilot magnitude ratios remainconstant during gain variations. Using the pilot magnitude estimation, again compensation factor may be computed and applied to each datasubcarrier to therefore compensate the data.

The number of pilots herein will be denoted by the variable N. The pilotindices run from 0 through N−1. The number of payload symbols is denotedby the variable M. The training symbol is assigned index 0. It should beappreciated that if there are several training symbols, they areaveraged to yield a single training symbol. The payload symbols areassigned indices 1, 2, 3 . . . M. The i^(th) pilot in the m^(th) OFDMsymbol is denoted by P_(m,i). The k^(th) data subcarrier in the m^(th)symbol is similarly denoted by X_(m,k). It should be noted that complexsignals are bold and italicized. Real signals are only bold. Variablesthat are not signals are only italicized. Estimates of unknownquantities are qualified with a tick (′). Hence, if H denotes a known(complex) signal, then H′ is an estimate of H. Magnitude of complexnumbers (i.e., their absolute value) is represented via the |·|operator.

An illustrative example of an embodiment of the present invention isdepicted in FIG. 7. The OFDM receiver 700 comprises all of thecomponents featured in OFDM receiver 600 of FIG. 6, with the addition ofa gain estimation and compensation device 701. FIG. 8 displays a blockdiagram of the computational steps taken by the gain estimation andcompensation device 701.

Gain estimation is achieved by first performing a ratio estimation 801.The ratio estimation step 801 is a time averaging technique, which maybe updated for every payload symbol. The ratio estimation step 801 maybe described using the following equation:

$\begin{matrix}{R_{m,i}^{\prime} = {\frac{1}{m}{\sum\limits_{j = 1}^{m}\;\left( {{P_{j,i}}/{P_{j,{lead}}}} \right)}}} & (1)\end{matrix}$

where R′_(m,i) represents the estimated ratio value of the pilots in theOFDM system; m represents the number of payload symbols included in theestimation; |P_(j,i)| represents the absolute value of the i^(th) pilotin the j^(th) payload symbol; and |P_(j,lead)| the absolute value of thelead pilot, or the pilot with the largest absolute value, in the j^(th)payload system. The training pilot with the highest power (i.e., withthe largest absolute value) is termed the lead pilot. The lead pilot isused as a reference when calculating relative pilot magnitude ratios.Its index is denoted by the subscript “lead.”

An example output from pilot magnitude ratio estimation 801 is providedbelow:

$\begin{matrix}{\lbrack i\rbrack^{b}\underset{\lbrack m\rbrack}{\begin{bmatrix}R_{1,4}^{\prime} & {{1/2}R_{2,4}^{\prime}} & {{1/3}R_{3,4}^{\prime}} & {{1/4}R_{4,4}^{\prime}} \\R_{1,3}^{\prime} & {{1/2}R_{2,3}^{\prime}} & {{1/3}R_{3,3}^{\prime}} & {{1/4}R_{4,3}^{\prime}} \\R_{1,2}^{\prime} & {{1/2}R_{2,2}^{\prime}} & {{1/3}R_{3,2}^{\prime}} & {{1/4}R_{4,2}^{\prime}} \\R_{1,1}^{\prime} & {{1/2}R_{2,1}^{\prime}} & {{1/3}R_{3,1}^{\prime}} & {{1/4}R_{4,1}^{\prime}}\end{bmatrix}}} & \left( {1A} \right)\end{matrix}$

where the ratio estimates are arranged horizontally by increasingpayload symbol number [m] and vertically by increasing pilot number [i].The pilot magnitude ratio is the absolute value of the pilot, for whichthe magnitude ratio is being estimated for, normalized by the absolutevalue of the lead pilot. Calculated averages of previously estimatedratios may also be taken into account and averaged over time for laterprocessed pilots. In other words, consider row b, the calculation ofR′_(4,3) yields the following:R′ _(4,3)=(¼)[R′ _(1,3) +R′ _(2,3) +R′ _(3,3) +|P _(4,3) |/P_(4,lead)|]  (1B)

In the example provided above, the estimated magnitude ratio for thepilot (i=3) in the symbol (m=4) is the average of all the previousestimates (for symbols m=1-3) for the same pilot (i=3), as well as thenormalized absolute value of the pilot for which the magnitude is beingestimated for (|P_(4,3)|/|P_(4,lead)|). Therefore, determining the pilotmagnitude estimation is achieved by obtaining the normalized value ofthe pilot in question and averaging that value over time, similarlyindexed pilots in previous symbols.

Next, the pilot magnitude, or variation in pilot magnitude, 803 iscomputed using the data obtained by the magnitude ratio estimation step801. The computation of the pilot magnitude 803 may be represented bythe following averaging formula:

$\begin{matrix}{A_{m,i}^{\prime} = {R_{m,i}^{\prime} \cdot {\left( {\sum\limits_{j = 1}^{N}\;{P_{m,j}}} \right)/\left( {\sum\limits_{j = 1}^{N}\; R_{m,j}^{\prime}} \right)}}} & (2)\end{matrix}$

where A′_(m,i) represents the estimated pilot magnitude, R′_(m,i)represents the pilot magnitude ratio estimation obtained in equation(1), and N is the total number of pilots in the m^(th) symbol. The pilotmagnitude estimate is obtained by summing the absolute value of all thepilots in the symbol and dividing that sum by the sum of all the pilotmagnitude ratio estimates obtained for the pilots in the symbol. Theresult is then multiplied by the pilot ratio estimation of the pilotwhose magnitude is being solved for. As an example, consider thefollowing example:

$\begin{matrix}{A_{2,2}^{\prime} = {R_{2,2}^{\prime}\left\lbrack \frac{{P_{2,1} + P_{2,2} + P_{2,3} + P_{2,4}}}{R_{2,1}^{\prime} + R_{2,2}^{\prime} + R_{2,3}^{\prime} + R_{2,4}^{\prime}} \right\rbrack}} & \left( {2A} \right)\end{matrix}$

where the estimated pilot magnitude for the pilot indexed as two (j=2)in the symbol indexed as two (m=2), is the estimated pilot magnituderatio of the pilot in question multiplied by the sum of the absolutevalue of all the pilots comprised in the symbol m=2, divided by the sumof all the estimated pilot magnitude ratio estimates obtained the symbolm=2. It should be appreciated that although the example illustrates onlyfour pilots per symbol, a symbol may comprise any number of pilots.Expanding and approximating the equation, the following results:

$\begin{matrix}{A_{2,2}^{\prime} = {R_{2,2}^{\prime}\left\lbrack \frac{{P_{2,1} + P_{2,2} + P_{2,3} + P_{2,4}}}{\frac{1}{2}\left\lbrack {\left( {\frac{P_{1,1}}{P_{1,{lead}}} + \frac{P_{2,1}}{P_{2,{lead}}}} \right) + \left( {\frac{P_{1,2}}{P_{1,{lead}}} + \frac{P_{2,2}}{P_{2,{lead}}}} \right) + {\frac{1}{2}\left( {\frac{P_{1,3}}{P_{1,{lead}}} + \frac{P_{2,3}}{P_{2,{lead}}}} \right)} + \left( {\frac{P_{1,4}}{P_{1,{lead}}} + \frac{P_{2,4}}{P_{2,{lead}}}} \right)} \right\rbrack} \right\rbrack}} & \left( {2B} \right) \\\begin{matrix}{A_{2,2}^{\prime} \approx {R_{2,2}^{\prime}\left\lbrack \frac{P}{\left( \frac{P}{P_{lead}} \right)} \right\rbrack}} \\{\approx {\frac{1}{2}{\left( {\frac{P_{1,2}}{P_{1,{lead}}} + \frac{P_{2,2}}{P_{2,{lead}}}} \right)\left\lbrack {P_{lead}} \right\rbrack}}} \\{\approx {\left( \frac{P}{P_{lead}} \right)\left\lbrack {P_{lead}} \right\rbrack}} \\{\approx {P}}\end{matrix} & \left( {2C} \right)\end{matrix}$

Therefore, through the use of averaging, equation (2) will yield thestrength or magnitude of the i^(th) pilot averaging over all the pilotsand pilot magnitude ratio estimates in the m^(th) payload symbol. Thus,equation (2) makes use of averaging over time with respect to payloadsymbols and averaging over frequency with respect to pilots. It shouldbe appreciated that the following simplified equation may also yield agood approximation of pilot magnitude estimation:

$\begin{matrix}{A_{m,i}^{\prime} = {\frac{1}{m}{\sum\limits_{j = 1}^{m}\;{P_{j,i}}}}} & \left( {2D} \right)\end{matrix}$

Equation 2D is the mathematically the same as equation (1) but for thenormalization with P_(lead). A few of the pilots in the payload symbolsmay be greatly affected by the gain variation such that their magnitudeis approximately equal to noise. Normalizing each pilot to the leadpilot will help to reduce the variations among pilots and reduce theamount of noise in the final estimation. Thus, as may be seen inequations (1)-(2D), a pilot magnitude may be obtained by averaging pilotsignals over successive symbols over time.

Finally, a gain compensation factor is computed 805. The computation ofthe gain compensation factor may be represented by the followingformula:C′ _(m,i) =|P _(0,i) |/A′ _(m,i)  (3)

where |P_(0,i)| is the absolute magnitude of the pilot indexed i at‘time zero,’ A′_(m,i) is the estimated pilot magnitude obtained duringthe processing life of the OFDM symbol and from equation (2), andC′_(m,i) is the gain compensation factor, or an estimated value of howmuch the pilot has changed in magnitude. Thus, the gain compensationfactor for an i^(th) pilot in an m^(th) symbol is obtained by obtainingthe ratio of the absolute value of the pilot at a ‘time zero,’ in thesymbol to be compensated, by the estimated pilot magnitude obtained forthe pilot in equation (2). Thus, in contrast to prior art systems, thegain compensation factor 805 adjusts the gain throughout the length ofthe OFDM packet and does not simply estimate the gain using ‘time zero’analyses. Therefore, mid-packet gain variations may be accounted for andcompensated.

The gain compensation factor is applied to all the data subcarriers inthe payload to compensate for changes in the front-end gain 807. Thecompensation of the data carriers may be represented by the followingformula:G _(m,k) =X _(m,k) C′ _(m,assoc(k))  (4)

where X_(m,k) represents the k^(th) data carrier in the m^(th) payloadsymbol, C′_(m, assoc(k)) represents the gain compensation which must beapplied to the data carrier, with the assoc(k) operator returning theindex of the pilot associated with data subcarrier k, and G_(m,k)represents the compensated data carrier. Thus, by applying the gaincompensation factor to the data subcarriers, variations due to gain maybe compensated for.

In the examples provided, equations (1)-(4) have been described as beingupdated for every incoming payload symbol. It should be appreciated thatequations (1)-(4) may be updated after a set number of payload symbolshave been processed. As was previously shown in FIG. 4, gain changes mayvary rapidly with time (i.e., f<0), or the gain changes may berelatively stable with time (i.e., f≧0). Therefore, an optimal number ofpayload symbols for updating may be determined based on the rate ofchange of gain variations. For example, estimation and compensationsteps may be updated for every payload symbol in the case of a rapidlychanging gain, or may be updated for every twenty payload symbols for arelatively stable gain. It may be advantageous to include multiplepayload symbols before updating estimation and compensationcalculations, since doing so will decrease the amount of noiseintroduced in the system.

The scheme discussed above is best suited for the ideal case in whichall pilots comprise an identical SNR. Frequently it may be the case thatone or more pilots comprise a SNR that is significantly lower than thatof the lead pilot. In fact, some pilots may be so severely faded thatthe faded pilots are comprised mostly of noise. Therefore, a significantamount of noise may be incorporated into the gain estimation andcompensation.

As was previously mentioned, normalization of pilots may help alleviatethe problem of severely faded pilot magnitudes but a more sophisticatedmethod further reduces the incorporation of noise in estimation andcompensation calculations. A pilot inclusion and exclusion method andalgorithm has been developed to eliminate pilot noise from gainestimation and compensation. The elimination of pilot noise isaccomplished by excluding pilots whose absolute magnitude has beengreatly reduced by gain variations. To determine which pilots are to beincluded or excluded, all pilots are ordered according to their absolutemagnitude values in the training symbol. Therefore, the lead pilot willalways have an index of zero and so on. The lead pilot will also alwaysbe included in the estimation calculations. Inclusion decisions of allthe other pilots are made in descending order of their strength. Apilot, indexed i, will be included if and only if the previous pilot, orthe pilot indexed i−1, has been included and if the following equation,or algorithm, is satisfied for the pilot indexed i:

$\begin{matrix}{{\; P_{0,i}} > {\left( {\sum\limits_{j = 0}^{i - 1}\;{\; P_{0,j}}} \right)\left( {\sqrt{\left( \frac{i}{\sum\limits_{j = 0}^{i - 1}\;{\; P_{0,j}}^{2}} \right)} - 1} \right)}} & (5)\end{matrix}$

where |P_(0,i)| represents the absolute value of the i^(th) pilot,

${\sum\limits_{j = 0}^{i - 1}\;{\; P_{0,j}}},{and}$$\sum\limits_{j = 0}^{i - 1}\;{\; P_{0,j}}^{2}$represent the sum and squared sum of the absolute value, respectively,of all pilots indexed 0-‘i−1.’

Alternatively, a simpler inclusion/exclusion scheme may be devised. Forexample, setting a threshold t, wherein t<1. All the pilots may bemultiplied by the threshold t, where only the pilots whose absolutemagnitude is greater than the lead pilot, upon multiplication by t, willbe included in the estimation. While more sophisticatedinclusion/exclusion strategies may allow for better performance, theimproved performance may come at the cost of additional hardware. Thus asuitable balance may be determined for individual signal processingneeds.

All the gain estimation and compensation steps, represented by equations(1)-(4) will remain the same for the included pilots. If the associatedpilot of a data carrier has been excluded, the closest included pilot tothat data carrier will be used for gain compensation.

A graphical representation of results, obtained in part by using theabove mentioned embodiments of the invention, is shown in FIG. 9. Thebenchmark represents a 54 Mbps packet error rate (PER) vs. SNR curve 900in a 50 ns multipath environment with no gain distortion. A curve with a−2 dB uncompensated gain variation 901 is also plotted. It is desirableto estimate and compensate for gain in order to close the gap 903between the benchmark curve 900 and the uncompensated −2 dB gainvariation curve 901, so that curve 903 may resemble the benchmark 900 asmuch as possible. Curves 905-908 show plotted data with 2 dB, 1 dB, −1dB, and −2 dB gain variations, respectively; whose gain has beenestimated and compensated according to an embodiment of the presentinvention. As may be seen from FIG. 9, curves 905-908 all show asignificant decrease in PER while maintaining a high SNR. Curves 905-908also over lap the benchmark curve 900 as well as decrease gap 903.

While this invention has been particularly shown and described withreferences to example embodiments thereof, it will be understood bythose skilled in the art that various changes in form and details may bemade therein without departing from the scope of the inventionencompassed by the appended claims.

What is claimed is:
 1. A method for determining a mid-packet gaincompensation to apply to a data subcarrier k within a symbol m of apacket in an orthogonal frequency division multiplexing (OFDM) system,the symbol m being one of a plurality of symbols within the packet andthe data subcarrier k being associated with a pilot indexed i of aplurality of pilots within the symbol m, the method comprising:determining a pilot magnitude ratio estimate for the pilot i of thesymbol m by normalizing the pilot i by an absolute value of a lead pilotwithin the symbol m; determining an estimate pilot magnitude for thepilot i by multiplying the pilot magnitude ratio estimate for the piloti of the symbol m by a sum of an absolute value of a plurality of pilotsin the symbol m, divided by a sum of pilot magnitude ratio estimates forthe plurality of pilots in the symbol m; and determining a gaincompensation factor to be applied to the subcarrier k associated withthe pilot i of the symbol m using the estimate pilot magnitude for thepilot i of the symbol m.
 2. The method of claim 1, wherein thedetermining a pilot magnitude ratio estimate for the pilot i of thesymbol m comprises averaging one or more previously calculated pilotmagnitude ratio estimates for similarly indexed pilots in previoussymbols and the normalized magnitude of the pilot i.
 3. The method ofclaim 1, wherein the determining the gain compensation factor to beapplied to the subcarrier k associated with the pilot i of the symbol mcomprises: dividing an absolute value of a pilot indexed i for thesymbol m at a time zero by the estimate pilot magnitude for the pilot iof the symbol m.
 4. An apparatus for determining a mid-packet gaincompensation to apply to a data subcarrier k within a symbol m of apacket in an orthogonal frequency division multiplexing (OFDM) system,the symbol m being one of a plurality of symbols within the packet andthe data subcarrier k being associated with a pilot indexed i of aplurality of pilots within the symbol m, the apparatus comprising: firstmeans for determining a pilot magnitude ratio estimate for the pilot iof the symbol m by normalizing the pilot i by an absolute value of alead pilot within the symbol m; second means for determining an estimatepilot magnitude for the pilot i by multiplying the pilot magnitude ratioestimate for the pilot i of the symbol m by a sum of an absolute valueof a plurality of pilots in the symbol m, divided by a sum of pilotmagnitude ratio estimates for the plurality of pilots in the symbol m;and third means for determining a gain compensation factor to be appliedto the subcarrier k associated with the pilot i of the symbol m usingthe estimate pilot magnitude for the pilot i of the symbol m.
 5. Theapparatus of claim 4, wherein, to determine a pilot magnitude ratioestimate for the pilot i of the symbol m, the first means averaging oneor more previously calculated pilot magnitude ratio estimates forsimilarly indexed pilots in previous symbols and the normalizedmagnitude of the pilot i.
 6. The apparatus of claim 4, wherein, todetermine the gain compensation factor to be applied to the subcarrier kassociated with the pilot i of the symbol m, the third means divides anabsolute value of a pilot indexed i for the symbol m at a time zero bythe estimate pilot magnitude for the pilot i of the symbol m.